QuestionWrite the equation for a function like $f(x)=|x|$ , shifted left 1 and down 9.
$g(x)=$

Studdy Solution

STEP 1

Assumptions1. The function $f(x)=|x|$ is the absolute value function. . The function $g(x)$ is a transformation of $f(x)$ .
3. Shifting one unit to the left means replacing $x$ with $x+1$ in the function.
4. Shifting nine units down means subtracting9 from the function.

STEP 2

Let's start by shifting the function one unit to the left. This can be done by replacing $x$ with $x+1$ in the function $f(x)=|x|$ .
$g(x)=|x+1|$

STEP 3

Now, let's shift the function nine units down. This can be done by subtracting9 from the function $g(x)=|x+1|$ .
$g(x)=|x+1|-9$ So, the equation for the function whose graph is the shape of $f(x)=|x|$ , but shifted one unit to the left and nine units down is $g(x)=|x+1|-9$ .

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